Detailed Question Description:
You should do multiple tests to be sure before answering!!

A person's dominant eye "is determined by subjective alignment of two objects presented at a stereodisparity far beyond Panum's area". There are a number of ways to do this:
-The Miles test. The observer extends both arms, brings both hands together to create a small opening, then with both eyes open views a distant object through the opening. The observer then alternates closing the eyes or slowly draws opening back to the head to determine which eye is viewing the object (i.e. the dominant eye).
-The Porta test. The observer extends one arm, then with both eyes open aligns the thumb or index finger with a distant object. The observer then alternates closing the eyes or slowly draws the thumb/finger back to the head to determine which eye is viewing the object (i.e. the dominant eye).
-The observer extends one arm, forms a small, circular opening with the thumb and index finger, then with both eyes open views a distant object through the opening. The observer then alternates closing the eyes or slowly draws the opening back to the head to determine which eye is viewing the object (i.e. the dominant eye).
-The Dolman method also known as the hole-in-the-card test. The subject is given a card with a small hole in the middle, instructed to hold it with both hands, then instructed to view a distant object through the hole with both eyes open. The observer then alternates closing the eyes or slowly draws the opening back to the head to determine which eye is viewing the object (i.e. the dominant eye).
-The convergence near-point test. The subject fixates an object that is moved toward the nose until divergence of one eye occurs (i.e. the non-dominant eye). It is an objective test of ocular dominance.
-Certain stereograms.
-The Pinhole test.
-The Ring test.
-Lens Fogging Technique. The subject fixates a distant object with both eyes open and appropriate correction in place. A +2.00 or +2.50 lens is alternately introduced in front of each eye, which blurs the distant object. The subject is then asked to state in which eye is the blur more noticeable. This is the dominant eye.
-The Camera Test. The subject brings a camera up to his/her face. Whichever eye is used to look through the viewfinder is the dominant eye.

Forced choice tests of dominance, such as the Dolman method, allow only a right or left eye result.

Both hemispheres control both eyes, but each one takes charge of a different half of the field of vision, and therefore a different half of both retinas. There is thus no direct analogy between "handedness" and "eyedness" as lateral phenomena.

In normal binocular vision there is an effect of parallax, and therefore the dominant eye is the one that is primarily relied on for precise positional information. This may be especially important in sports which require aim, such as archery, darts or shooting sports.

Approximately two-thirds of the population is right-eye dominant; however in a small portion of the population neither eye is dominant. Dominance does appear to change depending upon direction of gaze due to image size changes on the retinas. There also appears to be a higher prevalence of left-eye dominance in those with Williams-Beuren syndrome, and possibly in migraine sufferers as well. Eye dominance has been categorized as "weak" or "strong"; highly profound cases are sometimes caused by amblyopia or strabismus.

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